RMS velocity

Though the PIV image sequence is collected with a time spacing of 0.25 seconds, RMS velocity fluctuations in the near wake can still be obtained from them. The reasoning is that the near wake is dominated by large structures that in turn are associated with large time scales. A validation of PIV measurement of RMS velocity with hotwire data is reported in the doctoral thesis of Sunshanta Dutta available in this website.

The root mean square velocity (for a generic component u) at a location in the wake is calculated from the formula

The summation extends over samples, being the number of acquired velocity fields in time. Further, is the unsteady part of the velocity field that is given as

The time averaged velocity field U is determined by averaging the instantaneous velocity vectors using the formula